Week - 1 - Consistency of Units

Consistency of units – week 1 – LS Dyna

Aim: To convert the Given measurement values to different Unit Systems

Objective: Different industries use different system of units as per their convenience. The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed. For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.

• Purpose:- LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.
• Here's an example: Young's Modulus of steel is 210GPa which is input as 210e+9 in LS-DYNA as per SI unit system. However, if you use kg/mm/ms unit system, the input quantity will be 210. Thus, the conversion factor is 10^-9.

Value of the following measurements are given as follows:

• MASS 1kg
• LENGTH 1m
• TIME 1s
• FORCE 1N
• STRESS 1Pa
• ENERGY 1Nm
• DENSITY 1Kg/m3
• YOUNG'S Modulus 210GPa
• Velocity 56.33KMPH
• GRAVITY 9.8m/s2

Now, here are a few system of units:

• Kg cm ms
• Kg cm s
• gm mm ms
• kg m s
• g cm s
• g cm us
• g mm s
• ton mm s
• slug ft s
• kg mm s
• g cm ms
• kg mm ms

Conversions: (From SI unit to gm/mm/ms unit system)

MASS : 1kg = 1000gm

Conversion factor : 103

LENGTH : 1m = 1000mm

Conversion factor : 103

TIME : 1s = 1000ms

Conversion factor : 103

FORCE : 1N = 1kg*1 m/s2

= (1000g*1000mm)/(1000ms)2

= 106*10-6 (g*mm)/ms2

= 1 (g*mm)/ms2

Conversion factor : 1

STRESS : 1Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2)

= 1000g/{1000mm*(1000ms)2}

= 10-6 g/ (mm*ms2)

Conversion factor : 10-6

ENERGY : 1J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2)

= {1000g * (1000mm)2}/(1000ms)2

= (109 g*mm2) / (106 ms2)

= 103 (g*mm2/ ms2)

Conversion factor : 103

DENSITY : 1Kg/m3 = 1000g/(1000mm)3

= 10-6 g/mm3

Conversion factor : 10-6

YOUNGS MODULUS : 210GPa = 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2)

= 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2)

Conversion factor : 103

VELOCITY : 56.33 Kmph = 56.33 * {106mm/(3600*1000ms)}

= 15.647 mm/ms

Conversion factor : 5/18

GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)2

= 9.8* 10-3 mm/ms2

Conversion factor : 10-3

Table unit systems as rows and measured quantities as columns :

Unit system	Mass	Length	Time	Force	Stress	Energy
SI Unit kg m s	1kg	1m	1s	1 N = 1 kg*m/s2	1 Pa = 1 kg/(m* s2)	1 J = 1Nm = 1 kg*m2/s2
kg cm ms	1kg	102cm	103ms	10-4 kg*cm/ms2	10-8 kg/(cm*ms2)	10-2 kg*cm2/ms2
kg cm s	1kg	102cm	1s	102 kg*cm/s2	10-2 kg/(cm*s2)	104 kg*cm2/s2
g mm ms	103g	103mm	103ms	1 g*mm/ms2	10-6 g/(mm*ms2)	103 g*mm2/ms2
g cm s	103g	102cm	1s	105 g*cm/s2	10 g/(cm*s2)	107 g*cm2/s2
g cm μs	103g	102cm	106μs	10-7 g*cm/μs2	10-11 g/(cm*μs2)	10-5 g*cm2/μs2
g mm s	103g	103mm	1s	106 g*mm/ s2	1 g/(mm*s2)	109 g*mm2/s2
Ton mm s	10-3ton	103mm	1s	1 ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2
slug ft s	0.068slug	3.28 ft	1s	0.2246 slug*ft/ s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2
kg mm s	1kg	103mm	1s	103 kg*mm/s2	10-3 kg/(mm*s2)	106 kg*mm2/s2
g cm ms	103g	102cm	103ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2
kg mm ms	1kg	103mm	103ms	10-3 kg*mm/ms2	10-9 kg/(mm*ms2)	1 kg*mm2/ms2

Conclusion:

The Values are Converted into respected Unit System. Since Ls Dyna doesn't have a specific unit system the above assignment will be useful in deploying the Units while performing Simulation.